Differentiate.
-sin $\sqrt { x ^ { 4 } - 1 }$
A) cos $\sqrt { x ^ { 4 } - 1 }$
B) $\frac { 2 x ^ { 3 } \cos \sqrt { x ^ { 4 } - 1 } } { \sqrt { x ^ { 4 } - 1 } }$
C) 4 $x ^ { 3 }$ sin $\frac { 1 } { \sqrt { x ^ { 4 } - 1 } }$
D) $\frac { 1 } { 2 }$ sin $\frac { 1 } { \sqrt { x ^ { 4 } - 1 } }$

Question

Quizplus · Accepted Answer

To differentiate $sin(\sqrt{x^4 - 1})$, we use the chain rule. First, differentiate the outer function, $sin(u)$, with respect to $u$, which gives $cos(u)$. Then, differentiate the inner function, $\sqrt{x^4 - 1}$, with respect to $x$, which gives $\frac{2x^3}{2\sqrt{x^4 - 1}}$. Multiply these derivatives together to get the final answer: $\frac{2x^3 \cos(\sqrt{x^4 - 1})}{\sqrt{x^4 - 1}}$.

Differentiate x4−1\sqrt { x ^ { 4 } - 1 }x4−1​

Differentiate $\sqrt { x ^ { 4 } - 1 }$